How Math affects your thinking?

No, I'm not going to write cliches about how math makes you analytic, clever, etc... No no, instead I am going to describe a phenomenon that happens to me every now and then; I have maybe already told it to some of you.

Here is the phenomenon: You are trying to solve a ("real life") situation or make a decision. Suddenly, your subconsciousness comes in, shows you an "image" and "suggests" a solution.
As a (stupid) example: You want to go to a city and consider whether to go by bus or by bike. Suddenly, you "see" the bus schedule together with a coming-out-of-nothing feeling: "You stupid, look at the schedule! Sure you should go by bus."
In this particular case, the above mentioned "see" meant literally having the picture in your head (such as if you recall someone's face), but sometimes the "image" is something more abstract (but it still "feels" like a real image).

Now, why do I find this special? Of course I am used to that my subconsciousness influences my decisions. But it usually does so in a subtle way - by coloring my feelings and whispering things like "good idea", "strange", "bad idea". But in the above situation, the subconsciousness just breaks into my thoughts and starts shouting.
Why do I think my Math studies have been involved? The first reason is that I first started experiencing this when I was in my second year of Math studies. The second reason is that it happens sometimes (when I am lucky) when solving mathematical problems - you try to prove something and suddenly, out-of-nothing you just know which formulas you have to write down. Actually, the phenomenon probably happened to me for the first time when working on math. However, when working on math, it didn't feel strange (doing math is a weird and obscure business anyway...) - but it does feel strange in the "real life".

I remember talking about it twice with Palo (it seems such a long time ago now...). It seems that he experienced something like that as well, his interpretation was different though (it was not subconsciousness for him).

What do you think about it, dear readers? Do you experience something like this as well?